The quest to learn probabilistic automata and grammars is still ongoing.
Because of the known hardness results some restrictions need to be applied.
Recent works include an \({\textbf {L}^*}\)  learning algorithm for MDPs [1]}
(here the assumption is that states of the MDPs generate an observable output that allows identifying the current state based on the generated input-output sequence),
a passive learning algorithm for a subclass of PCFGs obtained by imposing several structural restrictions [2]}, [3]},
and using PDFA learning to obtain an interpretable model
of practically black-box models such as recurrent neural networks [4]}.
We have presented an algorithm for learning structurally unambiguous PCFGs from a given black-box language model using structured membership and equivalence queries.
To our knowledge this is the first algorithm provided for this question. Following the motivation of [4]}, the present work offers obtaining intrepretable models also in cases where the studied
object exhibits non-regular (yet context-free) behavior.
For future work, we think that improving our method to be more noise-tolerant would make the algorithm able to learn complex regular and context-free grammars from recurrent neural networks.



